Local bifurcation-branching analysis of global and “blow-up” patterns for a fourth-order thin film equation

摘要

Countable families of global-in-time and blow-up similarity sign-changing patterns of the Cauchy problem for the fourth-order thin film equation (TFE-4) $u_t=-nabla cdot left(|u|^n nabla Delta uright) quad {rm in} quad mathbb{R}^{N}timesmathbb{R}_{+} quad{rm where}quad n >0 ,$u_t=-nabla cdot left(|u|^n nabla Delta uright) quad {rm in} quad mathbb{R}^{N}timesmathbb{R}_{+} quad{rm where}quad n >0 ,